Download Rich Assessment Task on Probability

Rich Assessment Task on Probability
"Run of heads and tails”
Give students a situation of tossing up a coin, when we toss a coin, there are two
possibly outcomes. It can be either a head or a tail, which are both equally likely
(50% chance of each outcome). When we toss it a number of times we get any
sequence of Heads (H) and Tails (T). If we toss the coin a large number of times
you might expect the number of heads and the number of tails to be about equal.
However, when we repeatedly toss a coin we will also notice that we get runs of
heads and runs of tails of varying length. One possible outcome of tossing a coin
five times is HHHTH.
Investigation Project
This sequence HHHTH contains a run of three heads, a run of one tail, and a run
of one head, a total of three runs.
 Investigate the distribution of runs of and different length for the 5 coin
situation.
 How does the number of coin tosses affect the distribution of runs of
heads and tails?
 What if there was a different number of equally likely outcomes (for
example if you were rolling a dice instead of tossing a coin?
 Investigate the distribution of runs in these situations."
(Source: “Probability and Statistics in the Victorian Certificate of Education”)
Write up
1. List all the possible outcomes for these situations using simulation.
2. Investigate the affect of volume of trails on the outcomes and support all
your judgments with evidence.
3. Use of ICT technology to support your judgment.
Grades
Grades range from A to E, with A representing the highest standard and E
representing the lowest standard will be allocated as per following rubric.
A student
who
achieves
the grade
A
A student
who
achieves
the grade
B
Knowledge
Demonstrates
a very high
level of recall
of facts,
techniques
and formulae
regarding
Probability
and
Simulation.
Demonstrates
a high level of
recall of facts,
techniques
and formulae.
A student
who
achieves
the grade
C
Recalls most
facts,
techniques
and formulae.
A student
who
achieves
the grade
D
A student
who
achieves
the grade
E
Recalls some
facts,
techniques
and formulae.
Recalls some
facts,
techniques
and formulae.
Application
Selects,
extends and
applies
suitable
modelling
and problem
solving
techniques.
Argument
Uses mathematical
reasoning to develop
sound arguments in
support of
conclusions, results
and/or decisions,
justifies procedures.
Technology
Uses
required
technology
appropriatel
y and
effectively.
Selects and
applies
modelling
and problem
solving
techniques.
With
direction,
applies a
model.
Solves most
problems.
Solves some
problems.
Uses mathematical
reasoning to develop
logical arguments in
support of
conclusions, results
and/or decisions.
Uses some
mathematical
reasoning to develop
logical arguments.
Uses
required
technology
appropriatel
y and
effectively.
Uses
required
technology
appropriatel
y.
Solves some
problems
with
guidance.
Uses some
Uses
mathematical
required
reasoning to develop technology.
simple logical
arguments.
Uses some
required
technology.
Outcomes to be assessed
This Rich Assessment Task is related to Area of Study Unit 1 and 2 “Data
analysis and simulation”.
Data analysis and simulation
"Run of heads and tails” project will test student’s knowledge about
categorizing the given data and then interpreting that data into frequency tables
and bar charts for categorical data; dot plots.
the tested area of study covers the display, summary, and interpretation of
univariate and bivariate data, and the design, construction and evaluation of
probability simulation models.
This project will test students:
• Knowledge about representing categorical data and numerical data;
• Skills about displaying data of particular situation and then interpreting that data
to get desired results.
This project will test student’s knowledge about Simulation which includes:
• Random experiments, events and event spaces;
• Probability as an expression of long run proportion;
• Stages in using a simulation in a mathematical model: formulation, solution,
interpretation,
(Source: VCE study guide)
Rich assessment Task
"Run of heads and tails”
 Explicitly describe the expectations of the task to the learner, well
explained situations are provided and students just have to follow those
situations and provide their own understanding of “Probability and
Simulations”
 Project is designed to engage the learner as it has activities related to real
life situations.
 "Run of heads and tails” provide opportunities for students to
demonstrate subject knowledge, skills and understandings of “Probability
and Simulations”.
 This Project focuses on the critical areas of learning within Area of Study
Unit 1 and 2 “Data analysis and simulation”.
 This Project will assist teacher to determine the specific help which
students may require in content areas of “Probability and Simulations”.
 Assessment Rubric also reflects and cater key knowledge and its
applications of the topic as students will be assessed on the degree to
which they demonstrate:
1. Knowledge: - knowledge of mathematical facts, techniques and
formulas presented in the “Probability and Simulation”
2. Application: - appropriate selection and application of “Probability and
Simulation” skills in mathematical modelling and problem solving.
3. Argument: - the development of logical arguments to support solutions
4. Appropriate use of Technology
(Source: www.cirriculumsupport.education.nsw.gov.au )
Word Count--- 950
Reference List:
1. Gail FitzSimons and Robert Money “Probability and Statistics in
theVictorian Certificate of Education” Melbourne, Australia.
2. Rich assessment tasks: exploring quality assessment for the School
Certificate URL: www.cirriculumsupport.education.nsw.gov.au )
3. Jennifer Nolan Geoff Phillips Elena Iampolsky Sonja Stambulic Ross Allen
David Phillips “MATHS Quest for Year 11 SECOND EDITION” Jacaranda
Publications. 2000.
4. VCE Study Guide “General Mathematics” URL :
http://www.vcaa.vic.edu.au/vce/studies/mathematics/general/genmathinde
x.html